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Inradius of Isosceles Triangle given Legs and Base Angle Formula

GoCircumradius of Isosceles Triangle Formula

GoInradius of Isosceles Triangle Formula

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The Inradius of Isosceles Triangle is defined as the radius of the circle inscribed inside the Isosceles Triangle. Check FAQs

r i = S Legs \cdot \cos (∠ Base) \cdot \tan (\frac{∠ Base}{2})

r_i - Inradius of Isosceles Triangle?S_Legs - Legs of Isosceles Triangle?∠_Base - Base Angles of Isosceles Triangle?

Inradius of Isosceles Triangle given Legs and Base Angle Example

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Here is how the Inradius of Isosceles Triangle given Legs and Base Angle equation looks like with Values.

Here is how the Inradius of Isosceles Triangle given Legs and Base Angle equation looks like with Units.

Here is how the Inradius of Isosceles Triangle given Legs and Base Angle equation looks like.

2.1554 = 9 \cdot \cos (70) \cdot \tan (\frac{70}{2})

2.1554m = 9m \cdot \cos (70°) \cdot \tan (\frac{70°}{2})

2.1554 = 9 \cdot \cos (70) \cdot \tan (\frac{70}{2})

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Inradius of Isosceles Triangle given Legs and Base Angle Solution

Follow our step by step solution on how to calculate Inradius of Isosceles Triangle given Legs and Base Angle?

FIRST Step Consider the formula

r i = S Legs \cdot \cos (∠ Base) \cdot \tan (\frac{∠ Base}{2})

Next Step Substitute values of Variables

∴

r i = 9m \cdot \cos (70°) \cdot \tan (\frac{70°}{2})

Next Step Convert Units

∴

r i = 9m \cdot \cos (1.2217rad) \cdot \tan (\frac{1.2217rad}{2})

Next Step Prepare to Evaluate

∴

r i = 9 \cdot \cos (1.2217) \cdot \tan (\frac{1.2217}{2})

Next Step Evaluate

∴

r i = 2.15536574318662m

LAST Step Rounding Answer

∴

r i = 2.1554m

Inradius of Isosceles Triangle given Legs and Base Angle Formula Elements

Variables

Functions

Inradius of Isosceles Triangle

The Inradius of Isosceles Triangle is defined as the radius of the circle inscribed inside the Isosceles Triangle.

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inradius of Isosceles Triangle

Legs of Isosceles Triangle

The Legs of Isosceles Triangle are the two equal sides of the Isosceles Triangle.

Symbol: S_Legs

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Legs of Isosceles Triangle

Base Angles of Isosceles Triangle

Base Angles of Isosceles Triangle are the equal angles between the base and the legs of the Isosceles Triangle.

Symbol: ∠_Base

Measurement: AngleUnit: °

Note: Value should be between 0 to 180.

Formulas to find Base Angles of Isosceles Triangle

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

tan

The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle.

Syntax: tan(Angle)

Other Formulas to find Inradius of Isosceles Triangle

Go Circumradius of Isosceles Triangle

r i = \frac{{S Legs}^{2}}{\sqrt{4 \cdot {S Legs}^{2} - {S Base}^{2}}}

Go Inradius of Isosceles Triangle

r i = \frac{S Base}{2} \cdot \sqrt{\frac{2 \cdot S Legs - S Base}{2 \cdot S Legs + S Base}}

Go Inradius of Isosceles Triangle given Base and Height

r i = \frac{S Base \cdot h}{S Base + \sqrt{4 \cdot h^{2} + {S Base}^{2}}}

How to Evaluate Inradius of Isosceles Triangle given Legs and Base Angle?

Inradius of Isosceles Triangle given Legs and Base Angle evaluator uses Inradius of Isosceles Triangle = Legs of Isosceles Triangle*cos(Base Angles of Isosceles Triangle)*tan(Base Angles of Isosceles Triangle/2) to evaluate the Inradius of Isosceles Triangle, The Inradius of Isosceles Triangle given Legs and Base Angle formula is defined as the length of the radius of the incircle of Isosceles Triangle, calculated using its legs and base angle. Inradius of Isosceles Triangle is denoted by r_i symbol.

How to evaluate Inradius of Isosceles Triangle given Legs and Base Angle using this online evaluator? To use this online evaluator for Inradius of Isosceles Triangle given Legs and Base Angle, enter Legs of Isosceles Triangle (S_Legs) & Base Angles of Isosceles Triangle (∠_Base) and hit the calculate button.

FAQs on Inradius of Isosceles Triangle given Legs and Base Angle

What is the formula to find Inradius of Isosceles Triangle given Legs and Base Angle?

The formula of Inradius of Isosceles Triangle given Legs and Base Angle is expressed as Inradius of Isosceles Triangle = Legs of Isosceles Triangle*cos(Base Angles of Isosceles Triangle)*tan(Base Angles of Isosceles Triangle/2). Here is an example- 2.155366 = 9*cos(1.2217304763958)*tan(1.2217304763958/2).

How to calculate Inradius of Isosceles Triangle given Legs and Base Angle?

With Legs of Isosceles Triangle (S_Legs) & Base Angles of Isosceles Triangle (∠_Base) we can find Inradius of Isosceles Triangle given Legs and Base Angle using the formula - Inradius of Isosceles Triangle = Legs of Isosceles Triangle*cos(Base Angles of Isosceles Triangle)*tan(Base Angles of Isosceles Triangle/2). This formula also uses Cosine (cos), Tangent (tan) function(s).

What are the other ways to Calculate Inradius of Isosceles Triangle?

Here are the different ways to Calculate Inradius of Isosceles Triangle-

Inradius of Isosceles Triangle=Legs of Isosceles Triangle^2/sqrt(4*Legs of Isosceles Triangle^2-Base of Isosceles Triangle^2)
Inradius of Isosceles Triangle=Base of Isosceles Triangle/2*sqrt((2*Legs of Isosceles Triangle-Base of Isosceles Triangle)/(2*Legs of Isosceles Triangle+Base of Isosceles Triangle))
Inradius of Isosceles Triangle=(Base of Isosceles Triangle*Height of Isosceles Triangle)/(Base of Isosceles Triangle+sqrt(4*Height of Isosceles Triangle^2+Base of Isosceles Triangle^2))

Can the Inradius of Isosceles Triangle given Legs and Base Angle be negative?

No, the Inradius of Isosceles Triangle given Legs and Base Angle, measured in Length cannot be negative.

Which unit is used to measure Inradius of Isosceles Triangle given Legs and Base Angle?

Inradius of Isosceles Triangle given Legs and Base Angle is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Inradius of Isosceles Triangle given Legs and Base Angle can be measured.

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